Markov Chains and Probability Transition Models

How do we predict the future behavior of systems that change over time based on probability? Markov chains provide the mathematical framework to model everything from board games and weather patterns to search engine algorithms and financial markets. This text-only course guides you from the absolute basics of probability theory to the mathematical analysis of multi-state systems, equipping you with the tools to model and solve complex stochastic problems. What you'll learn: - Understand core terminology, random variables, and the fundamental Markov property - Calculate transition probabilities and construct multi-step transition matrices - Classify states as transient, recurrent, absorbing, or periodic - Determine steady-state distributions and analyze the limiting behavior of Markov systems - Explore modern computational applications, including basic Markov Chain Monte Carlo (MCMC) concepts - Practice solving analytical probability problems through structured, written step-by-step exercises You will begin by mastering essential definitions and probability concepts before moving on to matrix operations, state classifications, and long-term system analysis. This course is designed for beginners in statistics, data science, or quantitative fields, with no advanced prerequisites required. Start reading today to master the mathematical foundations of transition-based probability models.